CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
A STUDY OF DEFLAGRATION TO DETONATION TRANSITION IN A
MODEL A-B SYSTEM USING MOLECULAR DYNAMICS.
Justin Fellows, Peter J. Haskins and Malcolm D. Cook
Defence Evaluation & Research Agency, Fort Halstead, Sevenoaks, Kent, England TN14 7BP
Molecular Dynamics employing a model 2 dimensional molecular AB system has been used to study the
transition from burning through to detonation. In these studies a REBO (Reactive Empirical Bond Order)
potential was used to describe the interaction between the atoms. A small block of AB molecules was
given an initial temperature at the start of the simulation. The hot starting material was observed to
transfer energy to the adjacent cool material. After an initial induction period, reaction was observed at
the heated end, which released energy and produced product (A2 & B2) molecules. Much of this energy
was transferred to adjacent material that became hotter and subsequently reacted. These processes
continued and resulted in the growth of a hot unreacted region with products to one side and cold
unreacted material to the other. As the simulation progressed the hot unreacted zone was observed to
shorten and a shock wave developed which overtook the hot / cold interface and became a stable
detonation. Some parametric studies have been carried out to determine the critical conditions in this
model system for onset of a Deflagration to Detonation Transition (DDT).
INTRODUCTION
METHOD
It is of great practical importance to understand
how deflagration to detonation transitions (DDT)
emerge and propagate in energetic materials. In this
paper we have employed molecular dynamics to
examine the onset of such events in some model
systems. In particular, we have investigated the
critical conditions in these systems for the onset of a
DDT.
All the calculations reported here have been
carried out in 2D using a Reactive Empirical Bond
Order (REBO) potential. The form of this potential,
and its general properties have been described
elsewhere (1, 2, 3). In the results we report here, we
have followed Brenner et.al.1 in using the potential
of the form described here:
The object of this work has been to study, at a
fundamental level, how a thermal stimulus
manifests and affects the behaviour of a model
energetic material. Clearly the results and
conclusions drawn from this work are dependent on
the form of the model system chosen, and the
limitations and implications have been discussed in
previous papers (3).
where the many-body coupling term By is given by:
btj =
391
G
The calculations have been carried out using a
periodic boundary condition in the direction
orthogonal to the length of the material slab in order
to simulate an infinite width charge.
and the repulsive, bonding and non-bonding
interactions are given by:
Vr(rtj) = De exp(-/?V2S (/- - re)) I (S - 1)
Vb(ry) = SDe Qxp(-j3^2/S(rij
- re)) /(S-l)
DDT EVENTS
At the beginning of all these simulations, a slab
of material consisting of 576 atoms was set to have
the average kinetic energy equal to the stimulus
temperature. Parametric studies were then
performed to determine the critical conditions in the
model system for onset of a Deflagration to
Detonation Transition (DDT).
The smoothing function fc, given below,
provides a long range cut-off, and ensures there are
no discontinuities in the energy and forces:
for D\ < Ty < D2
Initially, the reaction exothermicity was set to
3eV/mol and an instantaneous starting temperature
of 5500K was used as the thermal stimulus. The hot
starting material was observed to transfer energy to
the adjacent cool material. After an initial induction
period, reaction was observed at the heated end,
which released energy and produced product (A2 &
B2) molecules. Much of this energy was transferred
to adjacent material that became hotter and
subsequently reacted (see Fig. 1 A). These processes
continued and resulted in the growth of a hot
unreacted region with products to one side and cold
unreacted material to the other. As the simulation
progressed, the hot unreacted zone was observed to
shorten and a shock wave developed which
overtook the hot / cold interface and became a
stable detonation (see Fig. IB).
= 1 , for rfj < Di
= 0 , for rtj > D2
The initial regular AB lattice was at zero
pressure and temperature, and atoms A and B,
although treated as chemically dissimilar, were both
assigned a mass of 14amu (nitrogen). The
remaining parameters were given the following
values:
p = 2.7 A°~l , re = l.QA°, S = 1.8, G = 5.0,
n = 0.5, m = 2.25A°~l, Anb = 0.09eV,
Bnb = 0.67 A°~l, D\ = 3.0A° , D2 = 4.0,4°.
De, the binding energy, or well depth, of the
molecules is the only parameter we have varied. We
took De(AB) = 2eV and De(A2) = De(E2) = 5eV as
our standard set, giving an overall exothermicity
(Q) for the reaction 2AB => A 2 + B2 of 3eV/mol.
frx&fiyFi
Coo! Unreacted
Hot Products A2 + B2
FIGURE 1A DDT part 1 (This figure is in color on the CD.)
392
Hot uoreact&d
to
mi
Detoimtkm Breaks Out
FIGURE IB DDT part 2 (This figure is in color on the CD.)
THRESHOLDS
Our first exercise was to examine the effect of
reaction exothermicity on the ability of the material
to undergo such a transition. Four cases were
explored in which the binding energy of the
products De(A2) = De(B2) took the values of 4eV,
5eV, 6eV and 7eV, (i.e. overall reaction
exothermicities of 2, 3, 4, 5eV). All the simulations
ran for 30 picoseconds, if no detonation occurred
within this time, a No DDT result was recorded.
DOT
Figure 2 shows the results from this preliminary
study, which shows an exponential type dependency
between Q and T. For the 2eV reaction we achieved
no DDT within the simulation times and
temperature ranges under investigation. It would
appear that for this model A-B system, a reaction
with Q=2eV is the limiting case where no DDT can
be induced within the timescale of these
simulations. This type of behaviour is very similar
to results published in a previous paper (3) where
shock initiation thresholds were explored.
Reaction Brthenridty(<A/)
FIGURE 2 Effect of Reaction Exothermicity (Q) on the
Temperature Thresholds for DDT
This phenomenon shows that chemical reactions
must be sufficiently fast and energetic enough in
order to support the initiation and growth of
detonation reactions.
393
Our second investigation explored the
dependence of run time to DDT on the reaction
exothermicity (Q) and the initiating temperature.
This induction time was recorded as the run time for
a full steady-state detonation wave to break out in
the material, (i.e. the point when the reactive shock
wave overtakes the hot unreacted region and meets
the cold unreacted material.)
REFERENCES
1. Brenner, D.W., Elert, M.L. and White, C.T.,
"Incorporation of reactive dynamics in simulations of
chemically-sustained shock waves", Proceedings of the
APS Topical Conference on Shock Compression of
Condensed Matter-1989, edited by S. C. Schmidt et al.,
North-Holland, Amsterdam, 1990, pp. 263-266.
2. Haskins, P.J., and Cook, M.D., "Molecular dynamics
studies of shock initiation in a model energetic material",
Proceedings of the APS Topical Conference on Shock
Compression of Condensed Matter-1993, edited by S. C.
Schmidt et al., AIP Conference Proceedings 309, New
York, 1994, pp. 1341-1344.
3. Haskins, P.J., Cook, M.D., Fellows, J., and Wood, A.,
"Molecular dynamics studies of fast decomposition in
energetic molecules", llth Symposium (International) on
Detonation, Office of Naval Research, ONR33300-5,
Snowmass, CO, 1998, pp.897-903.
4. Haskins, P.J., and Cook, M.D., "Molecular dynamics
studies of thermal and shock initiation in energetic
materials", Proceedings of the APS Topical Conference
on Shock Compression of Condensed Matter-1995, edited
by S. C. Schmidt et al., AIP Conference Proceedings 370,
New York, 1996, pp. 195-198.
5. Rice, B.M., Mattson, W., Grosh, J., and Trevino, S.F.,
Phys. Rev. E, 53, 623-635 (1995).
Figure 3 shows the induction time results for
values of Q=3,4,5eV in the temperature range of
1500K to 6500K. Again, these systems exhibit an
exponential style relationship between the
temperature and time to DDT. This behaviour is
reminiscent of an Arrhenius relationship between
reaction rate and temperature.
FIGURE 3 Effect of Temperature on the Induction Time for
Reactions with Differing Exothermicities (Q)
Using REBO potentials it has been concluded in
previous work (4, 5) that the predominant
detonation mechanism for these systems is densityinduced decomposition of the AB molecules,
followed by recombination to the product
molecules. Consequently, the failure to support a
DDT event below a critical exothermicity is
understandable in terms of the argument given
above. Whilst, in theory, thermal decomposition
should still allow a detonation to occur it is highly
probable that the duration required to initiate such a
process is far in excess of those considered in these
simulations.
394